private static final BigInteger TWO = BigInteger.valueOf(2);
private static final BigInteger THREE = BigInteger.valueOf(3);
private static final BigInteger FIVE = BigInteger.valueOf(5);

public static ArrayList<BigInteger> primeDecomp(BigInteger n){
    if(n.compareTo(TWO) < 0) return null;
    ArrayList<BigInteger> factors = new ArrayList<BigInteger>();

    // handle even values
    while(n.and(BigInteger.ONE).equals(BigInteger.ZERO)){
        n = n.shiftRight(1);
        factors.add(TWO);
    }

    // handle values divisible by three
    while(n.mod(THREE).equals(BigInteger.ZERO)){
        factors.add(THREE);
        n = n.divide(THREE);
    }

    // handle values divisible by five
    while(n.mod(FIVE).equals(BigInteger.ZERO)){
        factors.add(FIVE);
        n = n.divide(FIVE);
    }

    // much like how we can skip multiples of two, we can also skip
    // multiples of three and multiples of five. This increment array
    // helps us to accomplish that
    int[] pattern = {4,2,4,2,4,6,2,6};
    int pattern_index = 0;
    BigInteger current_test = BigInteger.valueOf(7);
    while(!n.equals(BigInteger.ONE)){
        while(n.mod(current_test).equals(BigInteger.ZERO)){
            factors.add(current_test);
            n = n.divide(current_test);
        }
        current_test = current_test.add(BigInteger.valueOf(pattern[pattern_index]));
        pattern_index = (pattern_index + 1) & 7;
    }

    return factors;
}